A343301 Numbers k such that 6*k+1 through 6*k+5 are all deficient (in A005100).

0, 1, 2, 5, 7, 8, 10, 12, 15, 19, 20, 21, 22, 24, 25, 27, 28, 30, 31, 35, 38, 39, 40, 41, 42, 44, 47, 48, 49, 52, 54, 55, 57, 59, 62, 64, 67, 68, 70, 71, 72, 75, 78, 80, 84, 85, 87, 89, 92, 94, 97, 98, 99, 100, 104, 105, 109, 110, 111, 112, 114, 115, 118, 119

Offset

1,3

Comments

Numbers k such that 6*k+1 is in A343302.

Note that no deficient number can be a multiple of 6.

Links

Jianing Song, Table of n, a(n) for n = 1..10000

Example

8 is a term since every one of 49, 50, 51, 52 and 53 is deficient.
157 is not a term since 943, 944, 946 and 947 are all deficient while 945 is not.

Mathematica

q[n_] := AllTrue[Range[5], DivisorSigma[-1, 6*n + #] < 2 &]; Select[Range[0, 120], q] (* Amiram Eldar, Mar 21 2024 *)

Prog

(PARI) isA343301(k) = for(i=1, 5, if( sigma(6*k+i) >= 2*(6*k+i), return(0) )); 1

Crossrefs

Cf. A005100 (deficient numbers), A343302, A343306.

Sequence in context: A025505 A285413 A184793 * A034028 A268272 A102700

Adjacent sequences: A343298 A343299 A343300 * A343302 A343303 A343304

Keyword

nonn

Author

Jianing Song, Apr 11 2021

Status

approved